I assume you have,

Are vector fields.

And you want to show,

And,

Thus, you need to show,

I do not want to type of this stuff out.

But consider you have in general,

.

(And they are well-behaved).

Now, just substitute that into both sides of the equation and show that they are true. I just do not want to do that because it is time consuming to type. It is really and easy proof, just substitute and see that the right hand and left hand match.